I am studying orbifolds with view towards Chen-Ruan cohomology. I have been struggling with inertia orbifolds but have no intuition about them at this point. I would appreciate your motivating me by answering the following questions:

1. What is the intuition behind inertia orbifolds? How should one think of them?
2. Why are inertia orbifolds important? What are the useful for?

Of course, given an orbifold, inertia orbifold comes for free. So it is indeed a natural mathematical object to think about. I hope to know some down-to-earth answers.

Thank you for sharing your ideas with me.